Buch, Englisch, 230 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 517 g
Buch, Englisch, 230 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 517 g
ISBN: 978-0-19-850784-0
Verlag: OUP Oxford
The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged.
The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
Weitere Infos & Material
- Preface
- Introduction
- 1: Gamma-convergence by numbers
- 2: Integral problems
- 3: Some homogenization problems
- 4: From discrete systems to integral functionals
- 5: Segmentation problems
- 6: Phase-transition problems
- 7: Free-discontinuity problems
- 8: Approximation of free-discontinuity problems
- 9: More homogenization problems
- 10: Interaction between elliptic problems and partition problems
- 11: Discrete systems and free-discontinuity problems
- 12: *Some comments on vectorial problems
- 13: *Dirichlet problems in perforated domains
- 14: *Dimension-reduction problems
- 15: *The 'slicing' method
- 16: *An introduction to the localization method of Gamma-convergence
- Appendices
- B: Characterization of Gamma-convergence for 1D(italic 'D') integral problems
- List of symbols
- References
- Index
